Asymptotic Stability Of A Class Of Nonlinear Discrete System Driven By Linear Feedback Control

In this paper,the asymptotic stability of the discrete model for a class of power integrator systems driven by a linear feedback controller is studied.For nonlinear dis-crete systems,Lyapunov's first method,also known as approximate linearization,is an effective method for stability analysis,but this method is not applicable to nonlinear discrete systems in the critical case.For critical case,Lyapunov's second method is can be used to analyze the asymptotic behavior of nonlinear discrete systems.Chetaev Instability Theorem of discrete systems is an important tool for stability analysis.However,it is a difficult problem to construct suitable Lyapunov\Chetaev functions.By using a system equivalent transformation,the required Lyapunov\Chetaev is ob?tained.By using Lyapunov Stability Theorem and Chetaev Instability Theorem,a necessary and sufficient conditions for the asymptotic stability is obtained.Moreover,a dual system model is proposed and a necessary and sufficient condition for the zero solution is obtained.Finally,the theoretical result is verified by a concrete numerical example.